Drug eluting 3D printed polymeric implants have great potential in orthopaedic applications since they are relatively inexpensive and can be designed to be patient specific thereby providing quality care. Fused Deposition Modeling (FDM) and Stereolithography (SLA) are among the most popular techniques available to print such polymeric implants. These techniques facilitate introducing antibiotics into the material at microscales during the manufacturing stage and subsequently, the printed implants can be engineered to release drugs in a controlled manner. However, FDM uses high temperature to melt the filament as it passes through the nozzle and SLA relies on exposure to nanoscale wavelength ultraviolet (UV) light which can adversely affect the anti-bacterial effectiveness of the antibiotics. The focus of this article is two-fold: i) Examine the effect of high temperature on the bacterial kill-effectiveness of eluted antibiotics through Polycaprolactone (PCL) based femoral implants and ii) Examine the effect of exposure to ultraviolet (UV) light on the bacterial kill-effectiveness of eluted antibiotics through femoral implants made up of a composite resin with various weight fractions of Polyethylene Glycol (PEG) and Polyethylene Glycol Diacrylate (PEGDA). Results indicate that even after exposing doxycycline, vancomycin and cefazolin at different temperatures between 20oC and 230oC, the antibiotics did not lose their effectiveness (kill radius of at least 0.85 cm). For doxycycline infused implants exposed to UV light, it was seen that a resin with 20 % PEGDA and 80 % PEG had the highest efficacy (1.8 cm of kill radius) and the lowest efficacy was found in an implant with 100 % PEGDA (1.2 cm of kill radius).

Costs associated with musculoskeletal diseases in the United States account for 5.7% of the Gross Domestic Product (GDP) (Weinstein et al. 2018). As such, there is a need to pursue new ideas in orthopaedic implants that can decrease cost and improve patient care. In the recent years, 3D printing of polymers using Fused Deposition Modeling (FDM) and metals using Direct Metal Laser Sintering (DMLS) has opened several exciting possibilities to create customized orthopaedic implants. Such implants can be engineered to release antibiotics in a controlled manner by infusing the drug into the material during manufacturing stage. However, the prevalence of high temperature could impact the anti-bacterial effectiveness of the eluted antibiotics in such implants. An alternative approach to circumvent this issue would be to modify the implant geometry to incorporate built-in design features such as micro-channels and reservoirs in which antibiotics can be introduced prior to the surgical procedure. Irrespective of the approach used, the ability of 3D printed orthopaedic implants to elute antibiotics, and the rate of elution are not well understood. The purpose of this article is to study the elution of doxycycline through 3D printed femoral implants using three different materials: Poly-Lactic Acid (PLA), Poly-Caprolactone (PCL) and Titanium grade Ti-6Al-4V. The PLA and Ti-6Al-4V implants were designed with built-in reservoirs and micro-channels in which doxycycline was introduced post the manufacturing stage. However, the PCL implants were printed from a PCL spool that was infused with doxycycline using an extruder. The PLA and Ti-6Al-4V experiments were run for a period of 31 days and the PCL experiment for one day. The antibacterial ability of eluted doxycycline from all implants were examined using Kirby-Bauer test on the bacteria E.coli k-12. The results show that most of doxycycline eluted through the three materials in the first 24 hours. After the initial spike, a steady release was achieved for the PLA and Ti-6Al-4V implants for 30 days. During this timeframe, Ti-6Al-4V implants released more doxycycline than the PLA implant. The eluted antibiotics through all the implants demonstrated the ability to kill bacteria in the subsequent Kirby-Bauer test. These outcomes show that irrespective of how the antibiotics were introduced, 3D printed polymeric and metallic implants have great potential in orthopaedic applications.

Under consideration is the finite-size scaling of the elastic properties in two-phase random polycrystals with individual grains belonging to any arbitrary crystal class. These polycrystals are generated by Voronoi Tessellations with varying grain sizes and volume fractions. Any given realization of such a microstructure sampled randomly is highly anisotropic and heterogeneous. Using extremum principles in elasticity, we introduce the notion of a ‘Heterogeneous Anisotropy Index \(\left( A^U_H\right) \)’ and examine its role in the scaling of elastic properties at finite mesoscales (\(\delta \)). The relationship between \(A^U_H\) and the Universal Anisotropy Index \(A^U\) by Ranganathan and Ostoja-Starzewski (Phys Rev Lett 101(5):055504, 2008) is established for special cases. The index \(A^U_H\) turns out to be a function of 43 variables—21 independent components for each phase and the volume fraction of either phase. The scale-dependent bounds are then obtained by setting up and solving 9250 Dirichlet and Neumann type boundary value problems consistent with the Hill–Mandel homogenization condition. Subsequently, the concept of an elastic scaling function is introduced that takes a power-law form in terms of \(A^U_H\) and (\(\delta \)). Finally, a material scaling diagram is constructed by employing the elastic scaling function which captures the convergence to the effective properties for any two-phase elastic microstructure.

In this paper, we develop unifying scaling laws describing the response of elastic polycrystals at finite mesoscales. These polycrystals are made up of individual grains belonging to any crystal class (from cubic to triclinic) and are generated by Voronoi tessellations with varying grain sizes. Rigorous scale-dependent bounds are then obtained by setting up and solving Dirichlet and Neumann boundary value problems consistent with the Hill–Mandel homogenization condition. The results generated are benchmarked with existing numerical results in special cases and the effect of grain shape on the scaling behavior is investigated. The convergence to the effective elastic properties with increasing number of grains is established by analyzing 5180 boundary value problems. This leads to the notion of an elastic scaling function which takes a power law form in terms of the universal anisotropy index and the mesoscale. Based on the scaling function, a material scaling diagram is constructed using which the convergence to the effective properties can be analyzed for any elastic microstructure.

Despite advances in contemporary micromechanics, there is a void in the literature on a versatile method for estimating the effective properties of polycrystals comprising of highly anisotropic single crystals belonging to lower symmetry class. Basing on variational principles in elasticity and the Hill-Mandel homogenization condition, we propose a versatile methodology to fill this void. It is demonstrated that the bounds obtained using the Hill-Mandel condition are tighter than the Voigt and Reuss [1,2] bounds, the Hashin-Shtrikman [3] bounds as well as a recently proposed self-consistent estimate by Kube and Arguelles [4] even for polycrystals with highly anisotropic single crystals. (C) 2017 Elsevier Ltd. All rights reserved.

In the United States, long standing deep infections of joint arthroplasty, such as total knee and total hip replacements, are treated with two-stage exchange. This requires the removal of the prior implant, placement of an antibiotic eluting spacer block made of polymethylmethacrylate (PMMA), followed by re-implantation of a new implant after treatment with intravenous antibiotics for six to eight weeks. Unfortunately, the use of PMMA as a spacer material has limitations in terms of mechanical and drug-eluting properties. PMMA is brittle and elutes most of the antibiotics within the first few days. Furthermore, the polymerization reaction for PMMA is highly exothermic, thereby limiting the use to heat-stable antibiotics. We hypothesize that the use of a 3D printed polymeric liner made of polylactic acid (PLA) would overcome the limitations of PMMA because it is a stronger and a less brittle material than PMMA. Furthermore, the liner can also act as a controlled drug delivery vehicle by using built in reservoirs and a network of micro-channels as well as by incorporating antibiotics directly into the polymer during manufacturing stage. Finally, the liner can be 3D printed according to the anatomy of the patient and thereby has the potential to transform the manner in which periprosthetic joint infections are currently treated.

The objective of this research is to generate design maps to identify functionally graded microstructures with enhanced fracture toughness. Several Functionally Graded Materials (FGMs) with an edge crack and membrane loading are considered and the resulting J-integral values are computed numerically using Finite Element Analysis. In order to capture the resulting stress fields accurately, Barsoum elements are used in the vicinity of the crack tip and the simulations are carried out for several crack lengths (a) and material contrasts (κ). The averages of the J-integral values are used to determine the normalized Stress Intensity Factors which are then benchmarked with existing analytical solutions in special cases. Furthermore, in order to facilitate an objective comparison between FGMs and homogeneous materials, a constraint is imposed on each of the microstructure so that the volume averaged modulus remains the same although the spatial variation is very different. Subsequently, we demonstrate that a FGM could perform either better or worse than the reference homogeneous material depending upon the crack length, the type of functional gradation and the material contrast (thereby the local gradient of the modulus at the crack tip). Finally, the notion of 'Fracture Index' is introduced using which 'design maps' are created in the (a−κ) space that reveal microstructures with enhanced fracture resistance. These maps are universal since any Functionally Graded Material can be mapped as a point on this space.

The problem of effective properties of material microstructures has received considerable attention over the past half a century. By effective (or overall, macroscopic, global) is meant the response assuming the existence of a representative volume element (RVE) on which a homogeneous continuum is being set up. Since the efforts over the past quarter century have been shifting to the problem of the size of RVE, this chapter reviews the results and challenges in this broad field for a wide range of materials. For the most part, the approach employed to assess the scaling to the RVE is based on the Hill-Mandel macrohomogeneity condition. This leads to bounds that explicitly involve the size of a mesoscale domain-this domain also being called a statistical volume element (SVE)-relative to the microscale and the type of boundary conditions applied to this domain. In general, the trend to pass from the SVE to RVE depends on random geometry and mechanical properties of the microstructure, and displays certain, possibly universal tendencies. This chapter discusses that issue first for linear elastic materials, where a scaling function plays a key role to concisely grasp the SVE-to-RVE scaling. This sets the stage for treatment of nonlinear and or/inelastic random materials, including elasto-plastic, viscoelastic, permeable, and thermoelastic classes. This methodology can be extended to homogenization of random media by micropolar (Cosserat) rather than by classical (Cauchy) continua as well as to homogenization under stationary (standing wave) or transient (wavefront) loading conditions. The final topic treated in this chapter is the formulation of continuum mechanics accounting for the violations of second law of thermodynamics, which have been studied on a molecular level in statistical physics over the past two decades. We end with an overview of open directions and challenges of this research field.

Piping is the main transportation method for fluids from one location to another within an industrial plant. Design and routing of piping is heavily influenced by the stresses generated due to thermal effects and high pressure of the operating fluid. In particular, pressurized fluids create critical loads on the supports and elbows of the pipe which increases the overall stresses in the piping. Moreover, long pipes operating under high temperature gradients tend to expand significantly. Therefore, designers and engineers usually provide an expansion loop in order to relieve the pipe from the critical stresses. However, expansion loops require extra space, supports, elbows, bends, additional steel structure that could adversely affect the operating cost. It is therefore necessary to optimize the geometry, the number of expansion loops, and the supports. Reducing the number of loops in one single system or reducing the length of the loop itself is always favored as long as stresses are within safe limits. Usually, the commercial software (PipeData) is used in the industry to get the dimensions of the expansion loop. However, this software is mostly based on empirical models that rely on past experience rather than engineering fundamentals. Accordingly, this paper conducts an optimization analysis concerning the expansion loop dimensions and the number of supports without compromising on the safety of piping. The design approach is conducted as per the guidelines of ASME B31.3 (Process Piping) code and uses the commercial software (CAESAR II) for stress calculations. A full comparison for the expansion loop dimension is conducted between the empirical approach and the optimization analysis using ASME B31.3 for one of the existing oilfield projects. Results indicate that optimization reduces the dimensions and the number of expansion loops as well as the total number of supports. This results in significant savings in the piping cost without any compromise on the safety.

Under investigation is the scale dependent electrical conductivity (and resistivity) of two-phase random checkerboards at arbitrary volume fractions and phase contrasts. Using variational principles, rigorous mesoscale bounds are obtained on the electrical properties at finite scales by imposing a boundary condition that is either uniform electric potential or uniform current density. We demonstrate the convergence of these bounds to the effective properties with increasing length scales. This convergence gives rise to the notion of a scalar-valued scaling function that accounts for the statistical nature of the mesoscale responses. A semi-analytical closed form solution for the scaling function is obtained as a function of phase contrast, volume fraction and the mesoscale. Finally, a material scaling diagram is constructed with which the convergence to the effective properties can be assessed for any random checkerboard with arbitrary phase contrast and volume fraction.

The buckling of slender columns with functionally graded microstructures is studied. In such columns, the flexural modulus is varied in a controlled manner along the column length. The objective is to identify microstructures that maximize (and minimize) the critical buckling load when compared to a reference homogeneous column. Several microstructures are examined and a constraint is imposed so that the volume averaged flexural modulus remains the same in all columns. The buckling load is determined using both the linear perturbation analysis as well as the Rayleigh-Ritz method. A relationship between the material distribution and the corresponding mode shape is established.

Purpose – The purpose of this paper is to study the statistics of thermal conductivity and resistivity tensors in two-phase random checkerboard microstructures at finite mesoscales. Design/methodology/approach – Microstructures at finite scales are generated by randomly sampling an infinite checkerboard at 50 percent nominal fraction. Boundary conditions that stem from the Hill-Mandel homogenization condition are then applied as thermal loadings on these microstructures. Findings – It is observed that the thermal response of the sampled microstructures is in general anisotropic at finite mesoscales. Based on 1,728 boundary value problems, the statistics of the tensor invariants (trace and determinant) are obtained as a function of material contrast, mesoscale and applied boundary conditions. The histograms as well as the moments (mean, variance, skewness and kurtosis) of the invariants are computed and discussed. A simple analytical form for the variance of the trace of mesoscale conductivity tensor is proposed as a function of individual phase conductivities and the mesoscale. Originality/value – A rigorous methodology to determine the evolution of the invariants of thermal conductivity (and resistivity) tensors across a variety of length scales (microscale to macroscale) is presented. The objective is to enable setting up of constitutive equations applicable to heat conduction that are valid across all length scales.

The scale-dependent homogenization is applied to a hyperbolic thermoelastic material with two relaxation times, where conductivity and stiffness are wide-sense stationary ergodic random fields. The previously established scaling functions for the Fourier-type conductivity and linear elastic responses are used to describe the trends to scale from the mesoscale statistical volume element level (SVE) to the (representative volume element) RVE level of a deterministic homogeneous continuum. In the case of white-noise type random fields, this finite-size scaling can be quantified via universally appearing stretched exponentials for conductivity and elasticity problems.

In this paper, microstructures-based constitutive relations are introduced to simulate the thermo-mechanical response of two nitrogen-alloyed austenitic stainless steels; Nitronic-50 and Uranus-B66, under static and dynamic loadings. The simulation of the flow stress is developed based on a combined approach of two different principal mechanisms; the cutting of dislocation forests and the overcoming of Peierls-Nabarro barriers. The experimental observations for Nitronic-50 and Uranus-B66 conducted by Gun and Nemat-Nasser (2006) and Frechard et al. (2008), respectively, over a wide range of temperatures and strain rates are also utilized in understanding the underlying deformation mechanisms. Results for the two stainless steels reveal that both the initial yielding and strain hardening are strongly dependent on the coupling effect of temperatures and strain rates. The methodology of obtaining the material parameters and their physical interpretation are presented thoroughly. The present model predicts results that compare very well with the experimental data for both stainless steels at initial temperature range of 77-1000 K and strain rates between 0.001 and 8000 s(-1). The effect of the physical quantities at the microstructures on the overall flow stress is also investigated. The evolution of dislocation density along with the initial dislocation density contribution plays a crucial role in determining the thermal stresses. It was observed that the thermal yield stress component is more affected by the presence of initial dislocations and decreases with the increase of the originated (initial) dislocation density. (C) 2014 Elsevier Ltd. All rights reserved.

Buckling is an instability encountered in a wide variety of problems, both in engineering and biology. Almost all engineering structures are designed with adequate safety factors to prevent failure due to buckling, yielding or dynamic loads. In a classical sense, design for buckling is done by carefully controlling the modulus of elasticity, moment of inertia and the length of the structure. Further, such an approach assumes the material to be homogeneous and does not generally account for the microstructural details of the column. In this paper, we study the buckling of inhomogeneous columns with a two-phase checkerboard microstructure. Monte Carlo simulations are used to generate microstructures with arbitrary volume fractions and phase contrasts (ratio of the modulus of individual phases). An analytical form is obtained for the ensemble averaged critical buckling load based on the results of over 18,000 eigenvalue problems at arbitrary volume fractions, phase contrasts and distributions. Further, microstructural realizations that correspond to the highest buckling load (best design) and the lowest buckling load (worst design) are identified and the corresponding distribution of individual phases is determined. Finally, the statistical nature of the critical buckling load is discussed by computing the statistical moments that include the mean and coefficient of variation.

Miniaturization and the need for novel materials with unique properties have driven composite materials to the forefront of research in solid mechanics. The response of a composite microstructure is dependent on the properties of individual phases, their distribution, the volume fractions and the scale of observation. The microstructures under investigation are sampled randomly from an infinite two-phase linear elastic planar checkerboard using a binomial distribution. A versatile methodology for investigating the effective response of such microstructures at finite scales is based on the Hill–Mandel macrohomogeneity condition. In this methodology, rigorous bounds are obtained as solutions to stochastic Dirichlet and Neumann boundary value problems from the level of a statistical volume element to that of a representative volume element (RVE). Within the framework of planar elasticity, the concept of a scaling function is introduced which unifies the treatment of several microstructures and quantifies the approach to RVE. It is demonstrated that the scaling function depends on the phase contrast and the mesoscale. Certain exact properties of the scaling function are derived rigorously, and its functional form is established using extensive numerical simulations on 163,728 microstructural realizations at varying contrasts, mesoscale and boundary conditions.